Most Americans comply with the tax laws, but every year many of our fellow citizens don't. The result is the "tax gap" -- the amount of revenue that the government loses because people are cheating. In one recent year, for example, the tax gap was $450 billion. That's a lot of money -- more than 10 times the budget of the State Department.

What can be done to increase compliance? Remarkably, a short letter to delinquent taxpayers -- based on the findings of behavioral science -- can have large effects. And the central lesson is simple: When tax delinquents are told that most people pay their taxes on time, they are far more likely to pay up. It's a nudge that can really work.

An important new study from the U.K. confirms the point. The study's lead author is Michael Hallsworth, a doctoral candidate at Imperial College London and an adviser to the U.K.'s Behavioural Insights Team. (Richard Thaler, my co-author of the book "Nudge," is an adviser to the Behavioural Insights Team.) In the first of two careful experiments, Hallsworth and his colleagues sent letters to more than 100,000 citizens in 2011. All of the letters noted that the recipients had not yet made correct tax payments, but there were different versions of what followed that reminder.

The first said: "Nine out of ten people pay their taxes on time." The second version said: "Nine out of ten people in the UK pay their taxes on time." The third said: "Nine out of ten people in the UK pay their taxes on time. You are currently in the very small minority of people who have not paid us yet." The fourth did not refer to social norms, but added this sentence: "Paying tax means we all gain from vital public services" such as the National Health Service, roads and schools.

The letters were exceedingly effective. Overall, those who received one of these letters were nearly four times more likely to pay their tax bill than those who did not. The most effective letter was the third: In less than a month, it produced $3.18 million in additional revenue. If that letter had been used across the entire sample, it would have produced an additional $18.9 million.

Hallsworth and his colleagues' second experiment involved nearly 120,000 taxpayers and more than a dozen different letters. Some of the letters referred to a general norm about existing practices (in social science parlance, a "descriptive norm"): "The great majority of people in the UK pay their tax on time." Other letters were more specific: "The great majority of people in your local area pay their tax on time" or "Most people with a debt like yours have paid it by now." Some of the letters referred to what people in the U.K. think taxpayers should do (in social science parlance, an "injunctive norm"): "The great majority of people agree that everyone in the UK should pay their tax on time," or "Nine out of ten people agree that everyone in the UK should pay their tax in time." Some of the letters emphasized that people could save money by paying now rather than later: "We are charging you interest on this amount."

With this experiment, Hallsworth and his colleagues replicated their earlier finding: "Norm" messages have a large impact. They also found that descriptive norms have a bigger effect than injunctive norms. Finally, highlighting a penalty that would increase over time made it more likely that people would pay.

Within a period of about three weeks, Hallsworth and his colleagues were able to generate about $15.24 million in additional tax revenue. Note that letters of this sort are essentially cost-free to produce and send, so the benefits of the intervention were easily justified.

How can these results be explained? The best answer is that people care whether they are acting morally. Their willingness to pay taxes, or to stop procrastinating, depends on whether the moral question is salient to them -- on whether they are incurring "moral costs." If the goal is to promote compliance, it helps if people learn that their fellow citizens think that they should. It helps even more if people learn that those who have not paid are part of a small minority of cheaters.

We don't yet know when and whether the Hallsworth study will generalize to different nations, but it fits with others that have found that people are less likely to engage in undesirable behavior (such as littering or theft) when they learn that it's out of line with what others do. In those studies, descriptive norms are also more powerful than injunctive norms.

Another interesting point to consider: Lamenting undesirable behavior can be counterproductive. If the goal is to reduce alcohol abuse, it may not be the best idea to announce that alcohol abuse is rapidly increasing, because people might think that heavy drinking is the social norm (and for that reason acceptable).

Sometimes tax authorities try to close the tax gap by threatening to punish delinquent taxpayers, but threats can create a political backlash, and enforcement can be expensive. There are no panaceas here, but we now know that a gentler approach can pay big dividends.

The message -- a small nudge -- should be: Pay your taxes, because the overwhelming majority of your fellow citizens are paying theirs.

Cass R. Sunstein, the Robert Walmsley university professor at Harvard Law School, is a Bloomberg View columnist.